The theory of measurement projection operators in grid-based time-dependent wave-packet calculations involving electronic continua in atoms and molecules is discussed. A hierarchy of projection operators relevant in their individual restricted configuration spaces is presented. At asymptotically large distances from the scattering or interaction center the projection operators involve plane waves only. To reach this asymptotic regime, however, large propagation times and large boxes may be required. At somewhat smaller distances from the scattering center, the projection operators are expressed in terms of analytical single-center Coulomb scattering waves with incoming wave boundary conditions. If propagation of the wave packet to these asymptotic regimes is impeded, the projection operators involve the exact scattering states which are not readily available in the wave-packet calculation and hence must be supplied by an additional, typically very demanding, calculation. The present approach suggests an exact way of analyzing the timely problem of the one-electron continuum in nonperturbative calculations. A key feature is that the propagated wave packet includes every interaction of the full Hamiltonian. The practicality of the proposed method is illustrated by the nontrivial example of strong-field ionization of the molecular hydrogen ion. Finally, the extension of the presented ideas to single and double ionization of two-electron systems is discussed.

We study vortical states in a Bose-Einstein condensate (BEC) filling a cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE) is derived in this setting, for the models with both repulsive and attractive interatomic interactions. Analytical formulas for the density profiles are obtained from the NPSE in the case of self-repulsion within the Thomas-Fermi approximation, and in the case of the self-attraction as exact solutions (bright solitons). A crucially important ingredient of the analysis is the comparison of these predictions with direct numerical solutions for the vortex states in the underlying 3D Gross-Pitaevskii equation. The comparison demonstrates that the NPSE provides for a very accurate approximation, in all the cases, including the prediction of the stability of the bright solitons and collapse threshold for them. In addition to the straight cigar-shaped trap, we also consider a torus-shaped configuration. In that case, we find a threshold for the transition from the axially uniform state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern, due to the instability in the self-attractive BEC filling the circular trap.

We study the photoassociation of Bose-Einstein condensed atoms into molecules using an optical cavity field. The driven cavity field introduces a dynamical degree of freedom into the photoassociation process, whose role in determining the stationary behavior has not previously been considered. The semiclassical stationary solutions for the atom and molecules as well as the intracavity field are found and their stability and scaling properties are determined in terms of experimentally controllable parameters including driving amplitude of the cavity and the nonlinear interactions between atoms and molecules. For weak cavity driving, we find a bifurcation in the atom and molecule number occurs that signals a transition from a stable steady state to nonlinear Rabi oscillations. For a strongly driven cavity, there exists bistability in the atom and molecule number.

Collective electron motion driven by intense laser pulses can become highly nonlinear as results of the $\mathbf{v}\times \mathbf{B}$ term in the Lorentz force and the relativistic mass increase effect. These nonlinear effects are the bases of many nonlinear phenomena in high-field physics. Using paraxial expansion we analyzed the three-dimensional collective relativistic motion of electrons driven by an intense pulsed Gaussian beam. We solved the three-dimensional velocity field and density field of the electrons, as well as the scalar potential field resulting from the electron density modulation, in terms of the vector potential of the laser pulse in the highly relativistic regime. From the solutions we derived an analytical expression for the nonlinear oscillation of the electric current density. The results are applied to a systematical analysis of coherent relativistic harmonic generation as a demonstration of the applications. Extensive comparison with published experimental data is made, and the remarkable agreement provides a strong support to the analysis presented in this paper.

We demonstrate a general weak-measurement model which allows Gaussian-preserving entanglement concentration of the two-mode squeezed vacuum. The power of this simple and elegant protocol is through the constraints it places on possible ancilla states and measurement strategies that will allow entanglement concentration. In particular, it is shown how previously discovered protocols of this kind emerge as special examples of the general model described here. Finally, as evidence of its utility, we use it to provide another example of such a protocol.

The ground-state wave function and the energy term of a relativistic electron moving in the field of two fixed centers, when interaction of this particle with centers is described by two Coulomb and two Coulomb-like scalar potentials are calculated analytically by the linear combination of atomic orbitals method. By means of perturbation theory the asymptotic expansions (at small and large internuclear distances $R$) of the eigenvalues $E\left(R\right)$ of the system for arbitrary states are obtained. The dependence of critical charge $Z_{\text{cr}}$ and critical distance $R_{\text{cr}}$ from the scalar coupling constant was investigated.

The spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material (LHM) is investigated. We first consider the case of the atom being in front of a LHM layer mounted on a mirror, where it has been claimed that the atomic decay would be inhibited completely. Here we introduce dispersion and dissipation in the LHM, and find that there are two factors that weaken the inhibition of spontaneous decay. One is atomic nonradiative decay at shorter distances and the other is the instantaneous radiative decay process for larger distances. Then we discuss the decay process of an atom embedded in a one-dimensional photonic crystal composed of alternate LHM and ordinary material [right-handed material (RHM)] layers (LHM-RHM PC). Because of two special characteristics of the LHM, phase compensation and the fact that a frequency with negative index is usual near the material resonance frequency, both the radiative and nonradiative decay processes in the LHM-RHM PC are much different from those in a RHM PC. Under appropriate condition, the population evolution of atoms in a LHM-RHM PC displays oscillatory behavior.

We study the detailed propagative characteristics of optical pulses in photonic band-gap (PBG) waveguides, coupled near resonantly to inhomogeneously broadened distributions of quantum dots. The line centers of the quantum-dot (QD) distributions are placed near a sharp discontinuity in the local electromagnetic density of states. Using finite-difference time-domain (FDTD) simulations of optical pulse dynamics and independent QD susceptibilities associated with resonance fluorescence, we demonstrate subpicosecond switching from pulse absorption to pulse amplification using steady-state optical holding and gate fields with power levels on the order of 1 milliwatt. In the case of collective response of QDs within the periodic dielectric microstructure, the gate power level is reduced to 200 microwatt for room temperature operation. In principle, this enables 200 Gbits per second optical information processing at wavelengths near 1.5 microns in various wavelength channels. The allowed pulse bandwidth in a given waveguide channel exceeds 0.5 THz allowing switching of subpicosecond laser pulses without pulse distortion. The switching contrast from absorption to gain is governed by the QD oscillator strength and dipole dephasing time scale. We consider dephasing time scales ranging from nanoseconds (low-temperature operation) to one picosecond (room-temperature operation). This all-optical transistor action is based on simple Markovian models of single-dot and collective-dot inversion and switching by coherent resonant pumping near the photon density of states discontinuity. The structured electromagnetic vacuum is provided by two-mode waveguide architectures in which one waveguide mode has a cutoff that occurs, with very large Purcell factor, near the QDs resonance, while the other waveguide mode exhibits nearly linear dispersion for fast optical propagation and modulation. Unlike optical switching based on Kerr nonlinearities in an optical cavity resonator, switching power levels and switching speeds for our QD device are not inversely proportional to cavity quality factors.

We address parametric down-conversion seeded by multimode pseudothermal fields. We show that this process may be used to generate multimode pairwise correlated states with entanglement properties that can be tuned by controlling the seed intensities. Parametric down-conversion seeded by multimode pseudothermal fields represents a source of correlated states, which allows one to explore the classical-quantum transition in pairwise correlations and to realize ghost imaging and ghost diffraction in regimes not yet explored by experiments.

The mechanism of the shift, broadening, and quenching of the ammonia inversion frequency with gas pressure has been a problem of lively interest for over $70\text{years}$. A simple quantum model of the ammonia molecule perturbed by collisions with ideal gas molecules displays the essential features of the experimental data for $\mathrm{N}{\mathrm{H}}_3$ and for $\mathrm{N}{\mathrm{D}}_3$. The model does not display the behavior expected from theories of environmental decoherence. On the other hand, models of perturbed classical oscillators do display behavior similar to our model and to experimental data. The quenching of the ammonia inversion transition cannot therefore be interpreted as spatial localization of the wave function.

We present an experimental observation of the electronic Doppler effect in resonant Auger spectra upon core excitation slightly above the carbon $K$ edge of the CO molecule. Thus the electronic Doppler effect has been identified in above-threshold excitation, and in a transition of $\Pi$ symmetry. Ab initio calculations of the potential energy curves of the relevant states of CO and the wave packet technique have been employed to provide a theoretical background to the experimental studies. The weak feature around $299.4\mathrm{eV}$ in the photoabsorption spectrum, whose decay has been investigated by the present experiment, is assigned to double (core-valence) excitations to C $1s$ shake-up states $\mid 1s_{\mathrm{C}}^{-1}1{\pi }^{-1}{\pi }^{*2}⟩$ with a strong dissociative character, and the Doppler splitting of the atomic peak has been reproduced by the simulation.

We study high-order harmonic generation in ${\mathrm{C}}_{60}$ molecules interacting with a linearly polarized intense short laser pulse at near- and mid-infrared wavelengths, using an extension of the so-called three-step or Lewenstein model to the molecular case. The results exhibit modulations in the plateaus of the spectra at the longer wavelengths, which are present for ensembles of aligned as well as randomly oriented fullerenes. The analysis of the results show that the minima can be explained by a multislit interference effect arising from the contributions of the 60 atomic centers to the dipole moment. Good agreement between the positions of the minima in the spectra obtained in the length gauge are found with those of the recombination matrix element, but not for those in the velocity gauge calculations. We further use a simple spherical model to analyze how geometrical information, such as the radius of the fullerene cage, can be obtained from the interference pattern in the harmonic spectra.

We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semianalytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.

We examine differences between various zero-group-velocity modes in photonic crystals, including those that arise from Bragg diffraction, anticrossings, and band repulsion. Zero-group velocity occurs at points where the group velocity changes sign, and therefore is conceptually related to “left-handed” media, in which the group velocity is opposite to the phase velocity. We consider this relationship more quantitatively in terms of the Fourier decomposition of the modes, by defining a measure of how much the “average” phase velocity is parallel to the group velocity—an anomalous region is one in which they are mostly antiparallel. We find that this quantity can be used to qualitatively distinguish different zero-group-velocity points. In one dimension, such anomalous regions are found never to occur. In higher dimensions, they are exhibited around certain zero-group-velocity points, and lead to unusual enhanced confinement behavior in microcavities.

We explore experimentally and numerically the physics underlying the optimization of high-order harmonic generation by intense laser pulses, whose temporal profile is tailored by a learning genetic algorithm. Based on a large set of optimization data obtained under different generation parameters, we show that the algorithm converges toward a class of very special profiles on the leading edge of the pulse. The behavior of the harmonic signal is then compared with theoretical simulations based on the time-dependent Schrödinger equation, allowing one to identify separately the role of microscopic and macroscopic phenomena in the temporal dynamics of high-harmonic generation and optimization.

The process of cascaded down-conversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analyzed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearized fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behavior when quantization of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.

The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a generalization of this bound (weak version of the Landau-Pollak uncertainty relation). Our generalization covers a pair of positive operator valued measures. A nontrivial but slightly weak inequality that can treat an arbitrary number of positive operator valued measures is also presented. A possible application to the problem of separability criterion is also suggested.

We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via a quantum nondemolition type of coupling, such that there is decoherence without dissipation, as well as when it interacts via a dissipative interaction, resulting in decoherence as well as dissipation. The system is taken to be either a two-level atom (or, equivalently, a spin-$1∕2$ system) or a harmonic oscillator, and the environment is modeled as a bath of harmonic oscillators, starting out in a squeezed thermal state. The impact of the different environmental parameters on the dynamics of the quantum phase distribution for the system starting out in various initial states is explicitly brought out. An interesting feature that emerges from our work is that the relationship between squeezing and temperature effects depends on the type of system-bath interaction. In the case of a quantum nondemolition type of interaction, squeezing and temperature work in tandem, producing a diffusive effect on the phase distribution. In contrast, in the case of a dissipative interaction, the influence of temperature can be counteracted by squeezing, which manifests as a resistance to randomization of phase. We make use of the phase distributions to bring out a notion of complementarity in atomic systems. We also study the variance of the phase using phase distributions conditioned on particular initial states of the system.

We show that a simple arrangement of external fields, consisting of a static component and an orthogonal rotating component, can continuously decouple a two-qubit entangled state from uncorrelated dephasing, bit flipping, and dissipation at finite temperature. We consider a situation where an entangled state shared between two noninteracting qubits is initially prepared and left to evolve under environmental perturbations and the protection of external fields. To illustrate the protection of the entanglement, we solve numerically a master equation in the Born approximation, considering independent boson fields at the same temperature coupled to the different error agents of each qubit.